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%I #22 Aug 01 2022 09:36:34
%S 21,224,1260,5040,16170,44352,108108,240240,495495,960960,1769768,
%T 3118752,5290740,8682240,13837320,21488544,32605881,48454560,70662900,
%U 101301200,142972830,198918720,273136500,370515600,496989675,659707776,867225744,1129719360,1459220840
%N a(n) = 7*(n+1)*binomial(n+5,7).
%C Number of 13-subsequences of [ 1, n ] with just 5 contiguous pairs.
%H Harvey P. Dale, <a href="/A027812/b027812.txt">Table of n, a(n) for n = 2..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F G.f.: 7*(3+5x)*x^2/(1-x)^9.
%F a(n) = C(n+1, 3)*C(n+5, 5). - _Zerinvary Lajos_, May 26 2005; corrected by _R. J. Mathar_, Feb 10 2016
%F From _Amiram Eldar_, Feb 04 2022: (Start)
%F Sum_{n>=2} 1/a(n) = 5*Pi^2/2 - 5909/240.
%F Sum_{n>=2} (-1)^n/a(n) = 5*Pi^2/4 - 32*log(2) + 791/80. (End)
%t Table[7 * (n+1) * Binomial[n+5, 7], {n, 2, 50}] (* _Amiram Eldar_, Feb 04 2022 *)
%t LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{21,224,1260,5040,16170,44352,108108,240240,495495},30] (* _Harvey P. Dale_, Aug 01 2022 *)
%K nonn,easy
%O 2,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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